Question
Pipe 'A' can fill a tank in 18 hours. Pipe 'B' is ____% as
efficient as pipe 'A'. If both pipes are opened simultaneously, the tank will be completely full in ____hours.The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true: I. 80, 10 II. 25, 14.4 III. 180, 6Solution
Let the capacity of the tank be '90x' litres. So, efficiency of pipe 'A' = 90x ÷ 18 = '5x' litres/hourFor: I
Efficiency of pipe 'B' = 5x × 0.80 = '4x' litres/hour
Time taken by both pipes together to fill the tank = 90x ÷ (4x + 5x) = 90x ÷ 9x = 10 hours
Therefore, statement 'I' is true.
For: II
Efficiency of pipe 'B' = 5x × 0.25 = '1.25x' litres/hour
Time taken by both pipes together to fill the tank = 90x ÷ (1.25x + 5x) = 90x ÷ 6.25x = 14.4 hours
Therefore, statement 'II' is true.
For: III
Efficiency of pipe 'B' = 5x × 1.80 = '9x' litres/hour
Time taken by both pipes together to fill the tank = 90x ÷ (9x + 5x) = 90x ÷ 14x ~ 6.43 hours
Therefore, statement 'III' is not true.
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